1. Field of Invention
The present invention relates to a communication system, and more particularly to a method and an apparatus for correlating complex number signals.
2. Description of Prior Art
In an existing communication system, in order to fulfill some basic functions, such as synchronization, channel estimation and the like, a receiver needs to correlate one received signal with one local reference signal to detect a correlation peak, thereby detecting a synchronization start and obtaining, for example, channel estimation. The received signal is usually obtained from a transmitted signal which has undergone channel transmission and local processing, such as RF (radio frequency) sampling, down conversion and A/D (analog-to-digital) conversion. The transmitted signal contains one special sequence, for example, a preamble or a trained sequence. Having experienced channel transmission and local processing, the special sequence forms part of the received signal. In addition, the special sequence is usually known to both of the transmitter and the receiver and pre-stored in the receiver as the local reference signal. Both the received signal and the local reference signal are generally complex number signals, that is, each symbol contained in the signals can be expressed by a complex number. The received signal R can be expressed as {R[i]=RRe[i]+jRIm[i], i={1, 2, . . . }}, and the local reference signal L can be expressed as {L[l]=LRe[l]+jLIm[l], l={1, 2, . . . }}, where RRe[i] and LRe[l] represent the real parts of the complex number symbols R[i] and L[l], respectively, and RIm[i] and LIm[l] represent the imaginary parts of the complex number symbols R[i] and L[l], respectively. In a conventional solution, the receiver performs complex number correlation on the received signal and the local reference signal so as to detect the correlation peak. The correlation operation on complex signal can be decomposed into a plurality of complex multiplications of two complex number symbols, and each complex multiplication can be further denoted as four real multiplications and two additions or subtractions, as shown in the following equation (1):
                                                                                          R                  ⁡                                      [                    m                    ]                                                  ×                                  L                  ⁡                                      [                    n                    ]                                                              =                            ⁢                                                (                                                                                    R                        Re                                            ⁡                                              [                        m                        ]                                                              +                                          j                      ⁢                                                                                          ⁢                                                                        R                          Im                                                ⁡                                                  [                          m                          ]                                                                                                      )                                ×                                  (                                                                                    L                        Re                                            ⁡                                              [                        n                        ]                                                              +                                          j                      ⁢                                                                                          ⁢                                                                        L                          Im                                                ⁡                                                  [                          n                          ]                                                                                                      )                                                                                                        =                            ⁢                                                (                                                                                                              R                          Re                                                ⁡                                                  [                          m                          ]                                                                    ×                                                                        L                          Re                                                ⁡                                                  [                          n                          ]                                                                                      -                                                                                            R                          Im                                                ⁡                                                  [                          m                          ]                                                                    ×                                                                        L                          Im                                                ⁡                                                  [                          n                          ]                                                                                                      )                                +                                                                                                      ⁢                              j                ⁡                                  (                                                                                                              R                          Re                                                ⁡                                                  [                          m                          ]                                                                    ×                                                                        L                          Im                                                ⁡                                                  [                          n                          ]                                                                                      +                                                                                            R                          Im                                                ⁡                                                  [                          m                          ]                                                                    ×                                                                        L                          Re                                                ⁡                                                  [                          n                          ]                                                                                                      )                                                                                        (        1        )            wherein R[m] and L[n] represent complex number symbols of the received signal and the local reference signal, respectively, RRe[m] and RIm[m] represent real part and imaginary part of the complex number symbol R[m], respectively, and LRe[n] and LIm[n] represent real part and imaginary part of the complex number symbol L[n], respectively.
The disadvantages usually incurred by implementing multiplication in hardware are that it takes a large area, consumes a high current and leads to expensive chip cost. In U.S. Pat. No. 5,365,549, proposed by Motorola and granted in November, 1994, a correlator and correlation method for complex signal are provided to perform complex correlation on one complex sampled signal and one reference signal so as to generate one complex correlation signal. In this method, the position of the reference signal relative to a real axis and an imaginary axis is determined at first, and the sampled signal is processed based on the determined position to generate real ad imaginary processed components. Next, the complex correlation signal is acquired by combining the real ad imaginary processed components. In this method, each multiplier is replaced with an adder, and hence the complex signal correlator is endowed with reduced complexity.
In order to reduce operation complexity and chip size, it is necessary to provide a correlation method and an apparatus thereof for complex signal, which can perform correlation on arbitrary complex signal, i.e., complex signal with arbitrary amplitude and radial angle.